Cache Creek Canyon Regional Park is a decent spot, about an hour drive from Davis. There's a good deal of wildlife roaming around including many wild turkey and waterfowl. Facilities are simple but not rustic. Swimming (at your own risk) in the river. There are 25 sites available on a first come first serve basis and 20 sites available by reservation only, as well as four group sites. It is fairly empty during winter and spring, but pretty crowded during summer and fall. Campsite rental is expensive at $25 per night, and there are additional fees for dogs, extra cars, and other things. Each site has a firepit with water faucets nearby. If you go there, the campsite is easy to miss so keep an eye out for the roadsigns as you will likely drive right past it. The campsite itself isn't anything special but the surrounding canyon is quite stunning.

About a mile upstream of the county camp site the land is managed by the BLM and primitive camping is allowed without a permit or fee. There's a decent flat area at the confluence of Bear Creek and Cache Creek that is convenient for primitive car camping and popular for launching kayaks.

You can also try KOA, which is camping for people who don't do camping. They tend to be mediocre, if you are used to camping at a decent state park for instance, but have facilities that many smaller state parks lack. In general though, they are to be avoided as they attract loud groups of annoying and sometimes shady people. KOA isn't for people who are looking for a destination, they are for people who need a place to stay immediately and don't want to spend the money on a hotel room.